# Mathematical Logic: Translate into predicate calculus symbols.

May you tell me if my "symbols" are correct? I am really suffering with this mathematical logic problem!

No sane witness would lie if his lying would implicate him in a crime. Therefore, if any witness implicated himself in a crime, then if all witnesses were sane, that witness did not lie.

This is my interpretation...

Premise:

(For all x) [(Lx implies Ix) implies [(Wx.Sx) implies (not Lx)]]

Conclusion:

(For all x) [(Wx and Sx) implies [(Wx implies Sx) implies (Wx implies (not Lx))]]

$\forall x ((Wx \land Ix) \rightarrow (\forall y (Wy \rightarrow Sy) \rightarrow \neg Lx))$